Central tendency. Which measure of central tendency is affected MOST by one extreme value?

1. The mode
2. The median
3. The mean
4. All three equally

Answer: The mean

The mean uses every value, so one very large or very small value drags it.

The median only depends on position, and the mode on frequency — neither is moved by a single outlier.

Central tendency. A data set has 20 values arranged in ascending order. In which position is the median?

1. The 10th value
2. The 11th value
3. Halfway between the 10th and 11th values
4. Halfway between the 9th and 10th values

Answer: Halfway between the 10th and 11th values

Median position = (n + 1) ÷ 2 = (20 + 1) ÷ 2 = 10,5.

Position 10,5 is not a real position, so average the 10th and 11th values.

Central tendency. Thirty test marks are grouped in intervals of 10. The interval 60–69 has the highest frequency (9 learners). What is the MODAL CLASS?

1. 9
2. 64,5
3. 60–69
4. It cannot be determined

Answer: 60–69

For grouped data you cannot see the individual values, so you cannot give a single mode.

You give the INTERVAL with the highest frequency instead.

Central tendency. For grouped data, which value represents each interval when you calculate the mean?

1. The lower boundary
2. The upper boundary
3. The midpoint of the interval
4. The frequency

Answer: The midpoint of the interval

Individual values are lost once data is grouped, so each interval is represented by its midpoint.

For 60–69 the midpoint is (60 + 69) ÷ 2 = 64,5.

Central tendency. Thirty marks are grouped and Σ(f × midpoint) = 1 845. Calculate the estimated mean.

1. 55,4
2. 61,5
3. 64,5
4. 1 845

Answer: 61,5

Estimated mean = Σ(f × midpoint) ÷ Σf

= 1 845 ÷ 30