Question

name:
date:
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

Explanation:

Step1: Calculate the Mean

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

Step2: Calculate the Median

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

Step3: Calculate the Mode

The mode is the most frequent value. All values appear once, so there is no mode (or all are modes with frequency 1). But typically, if no value repeats, we say no mode or all values are modes. Here, since each occurs once, we can state no mode or list all. But for this set, each value is unique, so mode: no mode (or each value 54, 63, 75, 77, 86 with frequency 1)

Answer:

Mean: \( 71 \), Median: \( 75 \), Mode: No mode (or each value occurs once)