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Which is the greatest, the mean, the mode, or the median of the data set? 11;11;12;12;12;12;13;15;17;22;22;22

Short Answer

Expert verified

Following are the results of the given data set, Mean of the data is 15.1, Median of the data is 12.5and Mode of the data is 12. Therefore, mean is greatest when compared to mode and median.

Step by step solution

01

Introduction

The Mean of the data is calculated by adding all numbers in the data set and then dividing by the number of values in the set.

The Median is the mid value of a data set and it is calculated by arranging the data set in ascending order (i.e., least to greatest).

The Mode is the most frequent number occurring in the data set.

02

Explanation

Mean:

As we given in Introduction part, mean is the average of given data set.

i.e.,

Mean =SumofthedataNumberofthedata

Mean=11+11+12+12+12+12+13+15+17+22+22+2212Mean=18112Mean=15.1

Median:

In the given data set, we have 12 numbers and that are sorted in ascending order (i.e., Least to greatest)

11;11;12;12;12;12;13;15;17;22;22;22

Here in this data set, 6th and 7th data are in the middle.

So, Median can be calculated in the following way:

Median =12+132

Medium =12.5

Mode:

As described in Introduction part, the most frequent data in the given data set is 12.

Therefore, the mode of this set is 12.

The value of Mean is greatest when compared to Median and Mode of this particular data set.

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