Question

The table below shows the distribution of dietary vitamin-A intake as reported by 14 students who filled out a dietary questionnaire in class.
The total intake is a combination of intake from individual food items and vitamin pills. The units are IU/100 (International Units/100)

Student Number	Intake (IU/100)	Student Number	Intake (IU/100)
1	38	8	46
2	22	9	31
3	22	10	11
4	94	11	42
5	18	12	35
6	45	13	55
7	103	14	82

a. Calculate the mean, median, mode for these data
b. Calculate the range and inter-quartile range for these data
c. Construct a stem-and-leaf plot using this data. Describe the shape of the distribution
d. Construct a box-plot for these data. Are there any outliers? If your answer is yes, identify the outliers.

Answer 1

a) Mean :

-----------------------------------------------------------------------------------------------------------

Median : Median is the middle value of the data, it is arranged in ascending / descending order.

11,18,22,22,31,35,38,42,45,46, 55, 82, 94, 103

So here median is average of 38 and 42.

------------------------------------------------------------------------------------

Mode : Mode is the most repeated value in the data.

Here 22 is most repeated value. So mode = 22 .

b) Range : Maximum value - minimum value = 103 - 11 = 92

---------------------------------------------------------------------------------------------------------------------

Inter-Quartile range = Q3 - Q1

Q1 = Median of the data below median .

Here data below median : 11,18,22,22,31,35,38

So here Q1 = 22

Q3 = Median of the data above median .

Here data below median : 42,45,46, 55, 82, 94, 103

So here Q3 = 55

Hence the interquartile range = Q3 -Q1 = 55 - 22 = 33

c) Stem -and - leaf plot :

1 | 1, 8

2 | 2, 2

3 | 1, 5, 8

4 | 2, 5, 6

5 | 5

6 |

7 |

8 | 2

9 | 4

10 |3

Here we can see that shape of distribution is right skewed.

d) Box plot :

Here no outlier found.