Question

Which of the following are important properties of the arithmetic mean? Check all that apply. Multiple select question. The mean is always less than the median. All of the values in the data are used in calculating the mean. Σ(X-X)=0 i.e. the sum of the deviations is zero. There is only one mean for a set of data. The mean can be calculated for nominal data.

Answer 1

Answer:

All of the values in the data are used in calculating the mean.

The sum of the deviations is zero.

There is only one mean for a set of data.

Step-by-step explanation:

Required

True statement about arithmetic mean

(a) False

The mean can be equal to, greater than or less than the median

(b) True

The arithmetic mean is the summation of all data divided by the number of data; hence, all values are included.

(c) True

All mean literally represent the distance of each value from the average; so,  when each value used in calculating the mean is subtracted from the calculated mean, then the end result is 0. i.e.$\sum(x - \bar x) = 0$

(d) True

The mean value of a distribution is always 1 value. When more values are added to the existing values or some values are removed from the existing values, the mean value will change.

(e) False

Nominal data are not numerical or quantitative data; hence, the mean cannot be calculated.