Answer:
Mean = 33.6, Median = 44, Range = 39, Midrange = 31.5, σ = 16.59.
Step-by-step explanation:
a) First, we will find the mean of the sample data;
Mean = 15+12+51+44+46 / 5
Mean = 33.6.
Second, we will find the median of the sample data;
for median you have to write your data set when in order from least to greatest then, the median is the middle number of the set:
12, 15, 44, 46, 51
Median = 44.
Third, we will find the range of the sample data;
Range is the difference between the highest and lowest values:
Range = 51 - 12
Range = 39.
Fourth, we will find the midrange of the sample data;
To find the midrange, add together the least and greatest values and divide by two, or in other words:
Midrange = 51+12 / 2
Midrange = 31.5.
Fifth, we will find the standard deviation of the sample data;
The formula of standard deviation is:
σ = √1/N Σi=1 to N (xi - mean)^2
now, subtract the mean and square the result
(15 - 33.6)^2 = 345.96
(12 - 33.6)^2 = 466.56
(51 - 33.6)^2 = 302.76
(44 - 33.6)^2 = 108.16
(46 - 33.6)^2 = 153.76
now, add them and divided by the number:
mean of squared differences = 345.96+466.56+302.76+108.16+153.76 / 5
mean of squared differences = 275.44
and Now, square root it, we will get standard deviation
σ = √275.44
σ = 16.59.
b) The 5-number summary;
minimum = 12
maximum = 51
median = 44
(12, 15,) 44, (46, 51)
Quartile1 = 13.5
Quartile3 = 48.5
Now, the summary is:
minimum = 12, Quartile1 = 13.5, median = 44, Quartile3 = 48.5, maximum = 51.
