Question

Can someone please check my work? If I made an error can you please correct me and show me the steps of how to get there? Also there were a couple problems I didn't know the answer to, can I get some help with those?

of 25 nrt below represent the speeds of 30 cars measured by radar on a city street with a pos sted 27 23 22 38 43 24 35 26 28 25 23 22 52 31 30 41 45 29 27 43 29 28 27 25 29 36 28 37 28 29 a. Create a stem-and-leaf plot Q122.3 3 y 556 77888g 999 301567 L 35 b. U se your calculator to find the following. Round to two decimal places. Mean Mcdian 285Mode 8Rage 30 Range Sample Standard Deviation/h3 Sample Variance 582 Population Standard Deviation c. Are there any values that would be considered outliers? Calculate the lower and upper limits (fences) and then identify any data values that would be considered outliers Potential Outliers 7. 2) What are three ifferent meaures of average? mode meah meian b) If the distribution of data is skewed, which measure of average is the best to use? id vanahs Hahderd dewatol What are three different measures of spread?

Answer 1

a) Stem and Leaf plot:

Stem	Leaf
2	223345567778888999
3	015678
4	1335
5	2

b) Mean: $\mu =\sum X_i/n=930/30=31$

Median: Middle most number: (n+1)/ th observation= (30+1)/2=15.5th observation

15.5 th observation= 15th observation+ 0.5(16th-15th)= 28+0.5(29-28)=28.5

Mode: Most repeated value: 28

Sample standard deviation: $S= \sqrt{\frac{\sum (x_i-\bar{X})^2}{n-1}}=7.62934$

Sample Variance: $S^2= \frac{\sum (x_i-\bar{X})^2}{n-1}=58.2069$

Population standard deviation: $\sigma = \sqrt{\frac{\sum (x_i-\mu )^2}{n}}=7.5011$

c)

Median: 31

Q1: (n+1)/4 th observation= 7.75 th observation= 25+0.75(26-25)=25.75

Q3: 3*(n+10/4 th observation= 23.25 th observation= 36+0.25(37-36)= 36.25

Interquartile range= Q3-Q1= 36.25-25.75= 10.5

Outliers:

Q1-1.5*IQR= 25.75- 1.5*10.5= 10

Q3+1.5*IQR= 36.25+1.5*10.5= 52

No outliers outside of 10 to 52.

7 a) Mean, Median and Mode

b) If the data is skewed, then MEDIAN is best to use. Because it represents middle most value.

c) Variance, standard deviation and range