Question

grade 7 measures of central tendency
expectation d1.5

1. calculate the mean, median, and mode for each data set;

a) 54, 86, 75, 77, 63
b) 150, 125, 143, 125, 148, 130, 168, 153

1. georgia recorded her test results in first term below:

75, 68, 73, 95, 76, 70

Explanation:

Part (a)

Step 1: Calculate the Mean

The mean is the sum of all values divided by the number of values. For the data set \(54, 86, 75, 77, 63\):
Sum \(= 54 + 86 + 75 + 77 + 63 = 355\)
Number of values \(n = 5\)
Mean \(= \frac{355}{5} = 71\)

Step 2: Calculate the Median

First, order the data set: \(54, 63, 75, 77, 86\)
Since \(n = 5\) (odd), the median is the middle value, which is the 3rd value. So median \(= 75\)

Step 3: Calculate the Mode

The mode is the value that appears most frequently. In this data set, all values appear once, so there is no mode (or we can say all values are modes with frequency 1).

Part (b)

Step 1: Calculate the Mean

For the data set \(150, 125, 143, 125, 148, 130, 168, 153\):
Sum \(= 150 + 125 + 143 + 125 + 148 + 130 + 168 + 153 = 1142\)
Number of values \(n = 8\)
Mean \(= \frac{1142}{8} = 142.75\)

Step 2: Calculate the Median

First, order the data set: \(125, 125, 130, 143, 148, 150, 153, 168\)
Since \(n = 8\) (even), the median is the average of the 4th and 5th values.
4th value \(= 143\), 5th value \(= 148\)
Median \(= \frac{143 + 148}{2} = \frac{291}{2} = 145.5\)

Step 3: Calculate the Mode

The mode is the value that appears most frequently. Here, \(125\) appears twice, and all other values appear once. So mode \(= 125\)

Answer:

• Part (a):
• Mean: \(71\)
• Median: \(75\)
• Mode: No mode (or all values with frequency 1)
• Part (b):
• Mean: \(142.75\)
• Median: \(145.5\)
• Mode: \(125\)