Question

The graph below displays how many pieces of candy Timmy and his five friends each received last Halloween. Within how many standard deviations of the mean do the values fall?

A. 1
B. 4
C. 2
D. 3

Answer 1

The correct option is C.

Explanation:

From the given graph it is clear that the pieces of candy received by Timmy and his five friends are

16, 19, 25, 32, 38, 40

The means of a data set is

`Mean=\frac{\sum{x}}{n}`

`Mean=(16+19+25+32+38+40)/(6)=(170)/(6)=28.33`

The means of the data is 28.33.

`Variance=\frac{\sum{x-Mean}^2}}{n}`

`\sigma^2=((16-28.33)^2+(19-28.33)^2+(25-28.33)^2+(32-28.33)^2+(38-28.33)^2+(40-28.33)^2)/(6)`

`\sigma^2=82.22`

`\sigma=√(82.22)`

`\sigma=9.068`

The standard deviations of the data is 9.068.

We have to find how many standard deviations of the mean do the values fall

The standard deviation for the means are

`(Minimum-mean)/(\sigma)=(16-28.33)/(9.068)=-1.36`

-1.36 means approx 2 standard dentition towards the right of mean.

`(Maximum-Mean)/(\sigma)=(40-28.33)/(9.068)=1.29`

1.29 means approx 2 standard dentition towards the left of mean.

Therefore the data values fall in 2 standard deviations of the mean.

Option C is correct.

Answer 2

(C)

Explanation:

First, we calculate the mean of the candies.

16,19,25,32,38,40

Mean = Sum of the candies/number of persons

= 170/6

=28.34

Variance = ∑(value - mean)^2

= (16-28.34)^2 + (19-28.34)^2+(25-28.34)^2+(32-28.34)^2+(38-28.34)^2+(40-28.34)^2/(n-1)

= 98.66

Standard deviation = √variance = √98.66 = 9.93

Now to calculate the standard deviation of the mean, we will calculate the difference between maximum value and mean. Also difference between between minimum value and mean

Maximum value-mean = 40-28.34 = 11.66

=11.66/9.93 = 1.17 towards the right of the mean

Minimum value-mean = -12.33

-12.33/9.93 = 1.24 towards the left of the mean

Hence the standard deviation of the mean in which the values fall is approximately 2.

C.) 2