By adding a constant value to every salary amount, the measures of
central tendency are increased by the amount, while the measures of
dispersion, remains the same
The correct responses are;
(a) <u>The shape of the data remains the same</u>
(b) <u>The mean and median are increased by $1,000</u>
(c) <u>The standard deviation and interquartile range remain the same</u>
Reasons:
The given parameters are;
Present teachers salary = Between $38,000 and $70,000
Amount of raise given to every teacher = $1,000
Required:
Effect of the raise on the following characteristics of the data
(a) Effect on the shape of distribution
The outline shape of the distribution will the same but higher by $1,000
(b) The mean of the data is given as follows;
Therefore, following an increase of $1,000, we have;
- Therefore, the new mean, is equal to the initial mean increased by 1,000
Median;
Given that all salaries, , are increased by $1,000, the median salary,
, is also increased by $1,000
Therefore;
- The correct response is that the median is increased by $1,000
(c) The standard deviation, σ, is given by ;
Where;
n = The number of teaches;
Given that, we have both a salary, , and the mean,
, increased by $1,000, we can write;
Therefore;
; <u>The standard deviation stays the same</u>
Interquartile range;
The interquartile range, IQR = Q₃ - Q₁
New interquartile range, IQR = (Q₃ + 1000) - (Q₁ + 1000) = Q₃ - Q₁ = IQR
Therefore;
- <u>The interquartile range stays the same</u>
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