Cards In This Deck

• $$\begin{gathered} \text{True or False?} \\ \text{In a histogram, the height of the bar represents the frequency of the class.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{Correct reasoning: The AREA of the bar represents the frequency.} \\ \text{The height represents the Frequency Density (}k\times \frac{Frequency}{ClassWidth}\text{)} \end{gathered}$$
• $\text{In a histogram question, you are given that a specific bar (width }w\text{, height }h\text{) represents frequency }f\text{. How do you find the frequency of another bar?}$
  $$\begin{gathered} \text{1. Calculate the area of the known bar (}{A}_1=w\times h\text{).} \\ \text{2. Establish the ratio }k=\frac{Frequency}{Area}\text{.} \\ \text{3. Calculate the area of the target bar (}{A}_2\text{).} \\ \text{4. Target Frequency = }k\times A_2\text{.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{In a histogram, the height of the bar always represents the frequency of the class.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct: The area of the bar represents the frequency (Frequency = Area / }k\text{). The height represents the Frequency Density.} \end{gathered}$$
• $\text{What is the formula for Frequency Density?}$
  $FrequencyDensity=\frac{Frequency}{ClassWidth}$
• $\text{First step when tasked to draw a stem and leaf diagram from raw data?}$
  $\text{Order the data (unless specifically asked for an unordered diagram, which is rare).}$
• $\text{When calculating Frequency Density for a histogram, how do you determine the class width for a class written as }10\le x<15\text{ versus }10-14\text{ (where data is rounded to the nearest integer)?}$
  $$\begin{gathered} \text{1. For }10\le x<15\text{: Width = }15-10=5\text{.} \\ \text{2. For }10-14\text{ (rounded): Use class boundaries. Lower bound 9.5, Upper bound 14.5. Width = }14.5-9.5=5\text{.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{On a box plot, the ’whiskers’ must always extend to the minimum and maximum values of the dataset.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct: If there are outliers, the whiskers extend to the highest/lowest values that are NOT outliers (or the outlier boundaries, depending on data availability). Outliers are marked separately with crosses.} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{In a back-to-back stem and leaf diagram, the leaves on the left-hand side are read from left to right (e.g., }|5|1\text{ represents 51).} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct: Leaves on the left are read outwards from the stem. If the stem is 5 and the leaf is 1 (written as }1|5|\text{), it represents 51, but the sequence }3 \\ 2 \\ 1|5|\text{ implies data points 51, 52, 53.} \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{When calculating the mean of grouped data, you must always use linear interpolation.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Method: Use the midpoint (}x\text{) of each class interval multiplied by frequency (}f\text{).} \end{gathered}$$
• $\text{What is the first step to calculate the combined mean of two data sets, Group A (size }{n}_1\text{, mean }{\bar{x}}_1\text{) and Group B (size }{n}_2\text{, mean }{\bar{x}}_2\text{)?}$
  $\text{Calculate the total sum of values for both groups: }\Sigma x_{total}=n_1{\bar{x}}_1+n_2{\bar{x}}_2\text{.}$
• $\text{When comparing two data sets (e.g., marks of two classes), which two key features must be mentioned to get full marks?}$
  $$\begin{gathered} \text{1. A measure of Location (Median or Mean).} \\ \text{2. A measure of Spread (IQR or Standard Deviation).} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{When comparing two data sets, it is valid to compare the Mean of one set with the Median of the other.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct: You must compare like with like.} \\ \text{- Use Mean \& Standard Deviation together (for symmetrical data).} \\ \text{- Use Median \& IQR together (for skewed data or data with outliers).} \end{gathered}$$
• $\text{Which measure of location (Mean, Median, or Mode) is preferred when the data is skewed or contains outliers?}$
  $\text{The Median}$
• $\text{When should you use the Median and IQR instead of the Mean and Standard Deviation to summarise a data set?}$
  $\text{When the data is skewed or contains extreme values (outliers).}$
• $$\begin{gathered} \text{Data }x\text{ is coded using }y=\frac{x-a}{b}\text{. You have calculated the mean of the coded data (}\bar{y}\text{). } \\ \text{How do you find the mean of the original data (}\bar{x}\text{)?} \end{gathered}$$
  $\bar{x}=b\bar{y}+a$
• $$\begin{gathered} \text{Data }x\text{ is coded using }y=\frac{x-a}{b}\text{. You have calculated the standard deviation of the coded data (} \\ {\sigma }_y\text{). } \\ \text{How do you find the standard deviation of the original data (} \\ {\sigma }_x\text{)?} \end{gathered}$$
  $$\begin{gathered} {\sigma }_x=b\times \\ {\sigma }_y \end{gathered}$$
• $\text{When calculating the Upper Quartile (}{Q}_3\text{) for discrete data list of size }n\text{, what is the first step?}$
  $$\begin{gathered} \text{Calculate }\frac{3n}{4}\text{.} \\ \text{* If result is not an integer: Round UP to choose that position.} \\ \text{* If result is an integer: Find the midpoint between that position and the next one.} \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{Standard Deviation can be negative if the data values are all negative.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Concept: Standard Deviation is always positive (or zero).} \end{gathered}$$
• $$\begin{gathered} \text{You are calculating the Lower Quartile (}{Q}_1\text{) for a discrete ordered list of }n\text{ data values. } \\ \text{You calculate }\frac{n}{4}\text{ and get a whole number (integer). What do you do?} \end{gathered}$$
  $\text{Find the midpoint between the }\frac{n}{4}\text{th value and the next value (}\frac{n}{4}+1\text{th value).}$
• $$\begin{gathered} \text{How does the Standard Deviation (} \\ {\sigma }_y\text{) change if the data is coded as }y=\frac{x-a}{b}\text{?} \end{gathered}$$
  $$\begin{gathered} {\sigma }_y=\frac{ \\ {\sigma }_x}{b} \end{gathered}$$
• $$\begin{gathered} \text{You are calculating the Upper Quartile (}{Q}_3\text{) for a discrete ordered list of }n\text{ data values. } \\ \text{You calculate }\frac{3n}{4}\text{ and get a decimal (non-integer). What do you do?} \end{gathered}$$
  $\text{Round up to the next whole number and pick that data point.}$
• $\text{How do you determine the position of the Lower Quartile (}{Q}_1\text{) from a discrete ordered list of }n\text{ data points (Stem and Leaf)?}$
  $$\begin{gathered} \text{Calculate }\frac{n}{4}\text{.} \\ \text{- If whole number: Pick the midpoint between this term and the next.} \\ \text{- If decimal: Round UP to the next whole number and pick that term.} \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ {S}_{xx}=\Sigma x^2-(\Sigma x{)}^2 \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Formula: }{S}_{xx}=\Sigma x^2-\frac{(\Sigma x{)}^2}{n} \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{In a table where ’Age’ is given as 25, 26, 27 (discrete integers), the class width for the group ’25’ is 0.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Width: 1 year (Boundary is 25.0 to 26.0)} \end{gathered}$$
• $$\begin{gathered} \text{True or False?} \\ \text{When using linear interpolation to find the median of grouped data, you use the stated class limits (e.g., 10-14, 15-19).} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{Correct reasoning: You must use the Class Boundaries (e.g., 9.5 and 14.5, 14.5 and 19.5) to close the gaps.} \end{gathered}$$
• $$\begin{gathered} \text{True or False? } \\ \text{For grouped data with class intervals 10-14 and 15-19, the upper class boundary for the first class is 14.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct Boundary: 14.5} \end{gathered}$$
• $\text{To use linear interpolation to find a median or percentile, what must you calculate for the frequency table first?}$
  $\text{Cumulative Frequency}$
• $\text{Using measures of location (Mean, Median, Mode), what is the typical condition for a distribution to be Negatively Skewed?}$
  $Mean<Median<Mode$
• $\text{What is the formula for calculating Skewness involving standard deviation (given in textbook)?}$
  $$\begin{gathered} \frac{3(Mean-Median)}{StandardDeviation} \\ \text{(Positive result = positive skew; Negative result = negative skew)} \end{gathered}$$
• $\text{Using quartiles (}{Q}_1,Q_2,Q_3\text{), what is the condition for a distribution to be Positively Skewed?}$
  $Q_3-Q_2>Q_2-Q_1$
• $$\begin{gathered} \text{True or False?} \\ \text{If a dataset contains an outlier calculated using }Mean\pm 2 \\ \sigma \text{, you should automatically remove it from the dataset before calculating the mean.} \end{gathered}$$
  $$\begin{gathered} \text{❌ False} \\ \text{✅ Correct: You only remove anomalies (clearly impossible values or errors). Legitimate extreme values (e.g., a very tall person) should be kept unless the question instructs to ’clean’ the data.} \end{gathered}$$
• $\text{You are asked to identify outliers in a dataset. How do you decide which formula to use?}$
  $$\begin{gathered} \text{Check the question carefully.} \\ \text{Common definitions include:} \\ \text{1. }{Q}_3+k(IQR)\text{ and }{Q}_1-k(IQR)\text{ (often }k=1.5\text{)} \\ \text{2. } \\ \mu \pm 2 \\ \sigma \\ \text{The exam question will explicitly state which rule to apply.} \end{gathered}$$