The median and mode are measures of central tendency.
The range is a measure of the spread of the data.
Calculating these from a grouped frequency table may be easier when the data set is very large.

Common misconception

That the interval widths need to be constant, or conversely that they can be anything.

If interested in people's ages it may be that decades makes sense once over 30 but that significant ages such as 16, 18 and 21 should form boundaries, depending on context. Encourage critical thinking for data with unequal intervals.

Keywords

Interval - An interval is all the values between two points.
Modal class - The modal class is the interval, or group of values, with the highest frequency in a data set.
Median class - The median class is the class which contains the central (middle) datum when the data are in numerical order.

When talking through tables always look at the interpretation of that table and link with what the summary statistic you are looking at means. Linking to context is really helpful to stop it becoming process driven and risk blurring of methods later.

Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.

Which of these describes the mode of a data set.

It is the sum of the values divided by the number of values.

It is the central piece of data when the data are in order of size.

Correct answer: It is value that appears most frequently in a data set.

Two values in a data set that occur most frequently an equal number of times.

Q2.

Match each summary statistic to its value for the data set: 2, 2, 2, 4, 7, 19

Correct Answer:mean,6

Correct Answer:median,3

Correct Answer:mode,2

Correct Answer:range,17

Q3.

Which of these statements are correct for this data set shown in a frequency table?

Correct answer: The modal value is 3.

The modal value is 4.

The modal value is 22.

Correct answer: The range is 2.

The range is 18.

Q4.

The table shows the number of rooms in some flats in a block of flats. The mean number of rooms in this data set is rooms.

Correct Answer: 4.5, 9/2, 4.5 rooms

Q5.

The median number of people in this data set is people.

Correct Answer: 3, 3 people

Q6.

Chocolate eggs are sold in boxes of either 2, 3, or 4. The number of boxes with each number of eggs is recorded. The mean of this data set is 3.5 eggs. The value of $$x$$ is .

Correct Answer: 20, twenty

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6 Questions

Q1.

Match each phrase to its definition.

Correct Answer:modal class,the interval with the highest frequency in a data set

the interval with the highest frequency in a data set

Correct Answer:median class,the interval which contains the central datum in an ordered data set

the interval which contains the central datum in an ordered data set

Correct Answer:mode,the most frequent data value in a data set

the most frequent data value in a data set

Q2.

What is the modal class of this data set?

Correct answer: $$30 \leq x < 40 $$

30 and 40

Q3.

This data set only contains integers. Which of these could be data points in the modal class?

Correct answer: 6

Correct answer: 7

7.5

Correct answer: 8

Q4.

The maximum possible range of this data set is .

Correct Answer: 230

Q5.

The average expected range of this data set is .

Correct Answer: 310

Q6.

Match each piece of information to its value.

Correct Answer:a,4

Correct Answer:b,20

Correct Answer:c,35

Correct Answer:median class,$$90 \leq x < 100 $$

$$90 \leq x < 100 $$

Correct Answer:modal class,$$100 \leq x < 105 $$

$$100 \leq x < 105 $$