Grade 10 · Core Mathematics · Lesson 6 of 16

Determining Median of Data and Introduction to Grouped Data Mean

A Grade 10 Core Mathematics CBE lesson from the sub-strand Statistics I. In it, learners determine the median of raw datasets with odd and even numbers of items.

Strand Statistics and ProbabilitySub-strand Statistics ILesson code 10CM-31-L640 minutes · 4 slides

KICD learning outcome (c)

Determine mean, mode and median of grouped and ungrouped data.

By the end of this lesson, learners should be able to

Determine the median of raw datasets with odd and even numbers of items.
Calculate the median from ungrouped frequency tables using cumulative frequency.
Compute mean, mode, and median from ungrouped frequency distribution tables.
Construct grouped frequency table columns for class midpoints $x$ and $f x$ to determine the mean of grouped data.

Key vocabulary

Median: middle value in a dataset when numbers are ordered from smallest to largest.; The median of the ordered scores five, seven, and nine is seven.
Cumulative frequency: running total of frequencies calculated by adding each frequency to the previous total.; The cumulative frequency reaching eight identifies the location of the median test score.
Frequency distribution: tabular arrangement showing how often each data value or interval occurs in data.; The frequency distribution displays student scores and how many learners achieved each score.
Class midpoint: average of the lower and upper boundaries of a given data class interval.; The class midpoint for interval ten to nineteen is calculated as fourteen point five.

Lesson preview

Slide 1 · Median of Raw Data (Odd vs. Even Datasets)Opening · 10 min

Figure 1: This diagram illustrates finding the median for an odd dataset by picking the middle value, and for an even dataset by averaging the two middle values.

Determining the median requires arranging numerical data in order of magnitude. For instance, when analysing the number of phone calls received by John and Everline per day in 7 and 10 days respectively, we deal with odd and even datasets. When a dataset contains an odd number of observations (7 days), the median is the exact middle value. When it contains an even number of observations (10 days), the median is calculated by finding the mean of the two central numbers. Examine Figure 1 to visualise how to find the median in both odd and even datasets.

For an odd number of items, such as phone calls over 7 days, the median is the single middle item.
When total items are even, such as phone calls over 10 days, average the two middle items.
Always arrange the raw data values in ascending or descending order before determining the middle positions.
For an even dataset of size $n$ , locate items at positions $\frac{n}{2}$ and $\frac{n}{2} + 1$ .

Worked example. Arrange the data in ascending order: 18, 20, 22, 24, 26, 28, 30, 32. Count the total number of items:

n = 8

, which is an even number. Identify the two middle positions:

\frac{8}{2} = 4^{th}

position and

\frac{8}{2} + 1 = 5^{th}

position. Locate the values at these positions:

4^{th}

value is 24, and

5^{th}

value is 26. Calculate the mean of the two middle values:

\frac{24 + 26}{2} = 25

. Answer: The median number of loaves sold is 25..

Check question: Find the median of the raw dataset: 14, 8, 18, 5, 20, 10.

12
11.5
10
12.5

Show answer

12. Sorting the 6 items in ascending order gives 5, 8, 10, 14, 18, 20. Since $n = 6$ is even, the middle values are at positions $3^{rd}$ (10) and $4^{th}$ (14). Their average is $\frac{10 + 14}{2} = 12$ .

Slide 2 · Finding Median from Frequency Tables using Cumulative FrequencyModel · 10 min

Figure 2: A frequency table demonstrates how to use a cumulative frequency column to locate the median position and find the corresponding data value.

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This lesson, and every other Grade 1–10 CBE lesson, comes ready to project with the EAP ClassKit. It runs without electricity or internet.

All 4 slides with diagrams and class activities
Teacher notes, SNE adaptations and assessment checks
Homework and the other 15 lessons in this sub-strand

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Determining Median of Data and Introduction to Grouped Data Mean

By the end of this lesson, learners should be able to

Key vocabulary

Lesson preview

Teach the full lesson on the projector

All 16 lessons in Statistics I