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What is the mode of the data set?


61, 92, 61, 89, 92, 61


What is the mean of the data set?


82, 105, 247, 119, 94, 202


At Sara's new job she spent $11.52, $6.48, $5.99, $14.00, and $9.50 on lunch the first week.


In the second week, she spent $4 more in total for the 5 lunches than the first week.


What is the increase in the mean for the second week compared to the first?




Round the answer to the nearest penny.



A class of 25 students took a spelling test. Two students scored 100 on each test, nine students scored 95 on each test, ten students scored 90 on each test, three students scored 80 on each test and one student scored 70.


What is the average score of the spelling test rounded to one decimal place?

Verified Answer :

What is the mode of the data set?: 61 (It's the one that repeats most often.)
Mean: 141.5 to find the mean add all of the the numbers then divide by how many numbers are there.

Answer:

1) 61, 92, 61, 89, 92, 61

Mode : The number which appears most often in a set of numbers.

61 occurred thrice

89 occurred once

92 occurred twice

Since 61 occurred most often

So, Mode of the given data is 61.

2)82, 105, 247, 119, 94, 202

Mean = \(\frac{\text{Sum of all observations}}{\text{Total no. of observations}}\)

So, Mean = \(\frac{82+105+247+119+94+202}{6}\)

Mean = \(141.5\)

Thus the mean of the given data is 141.5

3) First week expenditure:  $11.52, $6.48, $5.99, $14.00, and $9.50

Mean = @@MATH_TOKEN_3@@

So, Mean = @@MATH_TOKEN_4@@

Mean = @@MATH_TOKEN_5@@

Now we are given that in the second week, she spent $4 more in total for the 5 lunches than the first week.

So, Mean = \(\frac{\text{Sum of all observations+4}}{\text{Total no. of observations}}\)

So, Mean = \(\frac{11.52+6.48+5.99+14.00+9.50+4}{6}\)

Mean = \(8.581\)

Increase in the mean in the second week = 8.581-7.915 = 0.666

Hence the increase in the mean for the second week compared to the first is 0.666.

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