Question

Step 1: Describing and analyzing the dataSixth-grade students completed a random survey to determine how many songs eachstudent has downloaded to his/her media player in the past two months. The datagathered is represented in the table below.Music Downloads by Sixth GradersRespondentNumber1234on678910Girls50321556815018812255Boys754125227043124570a) Compute the measures of center for both the boys and girls data. Describe theirdifferences. Use the terms mean and median to justify your answer. (3 points)

Answer 1

a) Girls: Mean=46 Median=50 Mode=50 and 81

Boys: Mean=34 Median=33 Mode= None

Mean a good measure to give an idea of the whole but very sensitive to higher and lower figures inserted, on the table.

Median:

This is a measure more resistant to the lower and upper figures. Much more reliable.

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1) Let's compute the Measures of the Center, namely mean, median, mode:

Let's set a table, for the Music Downloads 6th graders, organizing it from the least to the greatest:

a) Let's calculate the Mean for the Girls

`x\text{ =}(50+32+15+56+81+50+18+81+22+55)/(10)=46`

Let's Calculate the Median:

This is a measure more resistant to the lower and upper figures. So a Median is more trustable in many times.

Since there 10 observations (even number) the Median for the girls are 50+ 50/2 = 50

The Mode, the number that repeats itself more often in this case, there are two 50 and 81 downloads. A bimodal observation. 2 modes.

For the boys:

Similarly for the boy, the Mean is the sum over 10 = 34

The Median for the boys is the sum of the 5th and 6th observation, over 2:

25+41/2 66/2=33

Mode

There is no mode. No number repeats itself for the boys.