⭐💡✏️NOTES: Representation of Data

Multiple Choice

Why is it important to use different methods for representing data in statistics?

• To make data look more interesting

• To confuse the audience

• To highlight different aspects and patterns in the data

• To avoid using numbers

Open Ended

Explain how you would use a stem and leaf diagram to compare the distribution of flower widths between two different plants of the same species.

Multiple Choice

What does the number '6 | 2 | 1' represent in the context of the twin stem and leaf diagram?

• 6.2 for plant 1 and 1 for plant 2

• 2.1 for plant 1 and 6.2 for plant 2

• 2.6 for plant 1 and 1.2 for plant 2

• 2.1 for plant 1 and 2.6 for plant 2

Fill in the Blanks

The inter-quartile range (IQR) is calculated as Q3 minus

.

Multiple Select

Which of the following steps are involved in calculating the inter-quartile range (IQR) from a stem and leaf diagram?

• Find the median (Q2)

• Find the lower quartile (Q1)

• Find the upper quartile (Q3)

• Subtract Q1 from Q3

Multiple Choice

According to the rules for identifying outliers, which value would be considered an outlier?

• A value greater than Q3 + 1.5(IQR)

• A value less than Q2 - 1.5(IQR)

• A value less than Q3 - 1.5(IQR)

• A value greater than Q1 + 1.5(IQR)

Open Ended

Given a stem and leaf diagram, describe the process for determining if a value is an outlier.

Multiple Choice

Which section of a box plot contains the median value?

• The section between the smallest value and lower quartile

• The section between the lower quartile and median

• The section between the median and upper quartile

• The section inside the box between the lower quartile and upper quartile

Open Ended

What is the process for identifying outliers in a box plot, and how is the acceptable range calculated?

Multiple Choice

Given the blood glucose data for 30 males, what is the interquartile range (IQR)?

• 1.4

• 3.6

• 4.7

• 1.1

Multiple Choice

When comparing two box plots, which two statistical measures should you always comment on?

• Mean and standard deviation

• Median and inter-quartile range

• Mode and range

• Variance and skewness

Fill in the Blanks

A histogram is different from a bar chart because there are no gaps between bars and the area of a bar is proportional to the

.

Multiple Choice

Based on the histogram data, which time interval had the highest frequency density?

• 25-30 mins

• 30-35 mins

• 35-40 mins

• 40-50 mins

Multiple Choice

Why is a histogram used to represent the time taken by students to complete a puzzle?

• Because time is continuous data

• Because time is discrete data

• Because time is categorical data

• Because time is ordinal data

Fill in the Blanks

Bar A in the histogram represents 78 children and has an area of 54.6 cm². The area representing 1 child is

cm².

Multiple Choice

Which of the following statements are true about the relationship between area and frequency in histograms?

• Area of each bar is proportional to frequency

• Area of each bar is proportional to time

• Area of each bar is proportional to the number of groups

• Area of each bar is proportional to the mean

Open Ended

Explain how the area of a bar in a histogram relates to the frequency of the data it represents.

Multiple Choice

If the total area of the histogram is 210 cm² and each child is represented by 0.7 cm², how many children were surveyed?

• 300

• 150

• 210

• 0.7

Open Ended

Describe the difference between symmetric, positive skew, and negative skew distributions as shown in the diagrams.

Multiple Choice

Which of the following statements about skewness is correct when Q2 - Q1 < Q3 - Q2 in a box plot?

• The data is symmetrical

• The data has positive skew

• The data has negative skew

• The mean equals the median

Open Ended

Explain how the measures of location (mean, median, mode) can be used to determine the type of skewness in a dataset.

Fill in the Blanks

Fill in the blank: A value of

for the skewness formula implies symmetrical data.

Multiple Choice

Which of the following formulas is used to calculate skewness based on mean, median, and standard deviation?

• (Mean - Median) / Standard Deviation

• 3(Mean - Median) / Standard Deviation

• (Mean + Median) / Standard Deviation

• 3(Median - Mean) / Standard Deviation

Multiple Choice

Given the stem-and-leaf plot and quartile calculations, which of the following are correct quartile values for the dataset?

• Q1 = 46, Q2 = 60, Q3 = 69

• Q1 = 45, Q2 = 57, Q3 = 68

• Q1 = 50, Q2 = 61, Q3 = 70

• Q1 = 48, Q2 = 59, Q3 = 67

Open Ended

Using the calculated mean, median, and standard deviation, determine the skewness of the data and explain what this indicates about the distribution.

Open Ended

How does a stem and leaf diagram help in organizing and interpreting data?

Open Ended

What are some different ways data can be visually represented, as shown in the images?