Question

A survey of 20 Middleton residents was done to determine the number of people in each household. The numerical frequencies are shown in the dot plot. A dot plot. The number line goes from 0 to 10. There is 1 dot above 1, 4 above 2, 5 above 3, 4 above 4, 4 above 5, 1 above 6, 0 above 7, 0 above 8, 1 above 9, 0 above 10. What is the outlier of this distribution? What is the mean of this data set? What is the range of this data set?

Answer 1

Answer:

minor outlier- 9

mean = 3.75

range is 8

Step-by-step explanation:

The data set would be:

1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 9 = 20 households

To calculate for the outlier in this data set:

Arrange all data points from lowest to highest

Calculate the median of the data set

Calculate the lower quartile and upper quartile

Find the interquartile range

Find the "inner fences" for the data set

So, our data has been arranged. The median of the data set is

    1, 2, 2, 2, 2, 3, 3, 3, 3,    3, 4,      4, 4, 4, 5, 5, 5, 5, 6, 9 = 3+4 / 2 = 7/2 = 3.5

Then we go on to find the lower and upper quartile

   1, 2, 2, 2, 2, 3, 3, 3, 3, 3,     (median)    4, 4, 4, 4, 5, 5, 5, 5, 6, 9

              lower quartile                                    upper quartile

median = 2+3 / 2 = 5/2 = 2.5             median = 5+5 / 2 = 10/2 = 5

Then finding interquartile range: upper quartile - lower quartile= 5 -2.5 = 2.5

To find the inner fences: multiply the interquartile range by 1.5. Then, add the result to upper quartile and subtract it from the lower quartile. Thus we have: 2.5*1.5 = 3.75.

add the result to upper quartile = 3.75 + 5 = 8.75

subtract it from the lower quartile = 3.75 - 2.5 = 1

Thus, the two inner fences are (1 - 8.75).

Thus, we can say that 9 is a minor outlier in this distribution and not a major one.

To find the mean :

lets make a table:

Number(x)    Frequency (f)    fx    

  1                  1                        1

  2                4                        8

  3                5                        15

  4                4                        16

  5               4                         20

  6               1                           6

  9               1                           9

summation of fx = 75 summation of frequency is 20.

Mean is summation of fx / summation of frequency = 75/20 = 3.75

Range of data set is the biggest data point - the smallest data point= 9 -1 = 8