Question

1. Section 3.1 Measures of Central Tendency pH in Water: The acidity of alkalinity of a solution is measured using pH. A pH less than 7 is acidic; a pH greater than 7 is alkaline. The following data represent the pH in samples of bottled water and tap water. Tap 7.64 7.45 7.47 7.50 7.68 7.69 7.45 7.10 7.56 7.47 7.52 7.47 Bottled 5.15 5.09 5.26 5.20 5.02 5.23 5.28 5.26 5.13 5.26 5.21 5.24 a) Determine the mean, median and mode pH for each type of water. b) Comment on the differences between the two water types. c) Suppose the pH of 7.10 in tap water was incorrectly recorded as 1.70. How does this affect the mean

Answer 1

Answer:

For tap water

Mean = 7.5

Median = 7.485

Mode = 7.47

For bottled water

Mean = 5.1942

Median = 5.22

Mode = 5.26

b) Tap water is alkaline while bottled water is acidic

c) For 7.10 recorded as 1.70, mean value will decrease to 7.05

Step-by-step explanation:

Given;

pH readings for tap water

7.64, 7.45, 7.47, 7.50, 7.68, 7.69, 7.45, 7.10, 7.56, 7.47, 7.52, 7.47

Now,

Mean = $\frac{\textup{Sum of all readings}}{\textup{Number of readings}}$

Sum of all readings

= 7.64 + 7.45+ 7.47+ 7.50+ 7.68+ 7.69+ 7.45+ 7.10+ 7.56+ 7.47+7.52+7.47

= 90

Number of readings = 12

or

Mean = $\frac{90}{12}$

or

Mean = 7.5

For median

Putting the data set in ascending numerical order

7.10 , 7.45, 7.45, 7.47, 7.47, 7.47 , 7.50, 7.52, 7.56, 7.64 , 7.68, 7.69

Thus,

median = $\frac{\textup{7.47+7.50}}{\textup{2}}$ = 7.485

Mode = number that appears most frequently = 7.47

Now for bottled water

Readings are :

5.15 5.09 5.26 5.20 5.02 5.23 5.28 5.26 5.13 5.26 5.21 5.24

Mean = $\frac{\textup{Sum of all readings}}{\textup{Number of readings}}$

Sum of all readings =

5.15 + 5.09 + 5.26 + 5.20 + 5.02 + 5.23 + 5.28 + 5.26 + 5.13 + 5.26 + 5.21 + 5.24

= 62.33

Number of readings = 12

Mean = $\frac{\textup{62.33}}{\textup{12}}$

or

Mean = 5.1942

Putting the data set in ascending numerical order

5.02, 5.09,  5.13, 5.15, 5.20, 5.21, 5.23, 5.24, 5.26, 5.26, 5.26, 5.28

median = $\frac{\textup{5.21 +5.23}}{\textup{2}}$ = 5.22

Mode = number that appears most frequently = 5.26

b) Tap water is alkaline while bottled water is acidic

c) For 7.10 recorded as 1.70

Mean = $\frac{\textup{Sum of all readings}}{\textup{Number of readings}}$

Sum of all readings

= 7.64 + 7.45+ 7.47+ 7.50+ 7.68+ 7.69+ 7.45+ 1.70+ 7.56+ 7.47+7.52+7.47

= 84.6

Number of readings = 12

or

Mean = $\frac{84.6}{12}$

or

Mean = 7.05

Hence , the mean value will decrease to 7.05