Answer:
1) D. 3.55
2) A
Step-by-step explanation:
Question 1
To find the variance for the given data, first calculate the mean (average) of the data set.
[tex]\textsf{Mean} = \dfrac{17.0 + 15.2 + 18.5 + 13.6 + 13.8}{5} = \dfrac{78.1}{5} = 15.62[/tex]
Subtract the mean from each data point and square the result:
[tex](17.0 - 15.62)^2 = 1.9044[/tex]
[tex](15.2 - 15.62)^2 = 0.1764[/tex]
[tex](18.5 - 15.62)^2 = 8.2944[/tex]
[tex](13.6 - 15.62)^2 = 4.0804[/tex]
[tex](13.8 - 15.62)^2 = 3.3124[/tex]
Find the average of the squared differences.
[tex]\begin{aligned}\textsf{Variance} &= \dfrac{1.9044+0.1764+8.2944+4.0804+3.3123}{5}\\\\&= \dfrac{17.768}{5}\\\\&=3.5536\\\\&=3.55\; \sf (2\;d.p.)\end{aligned}[/tex]
Therefore, the variance rounded to two decimal places is 3.55.
[tex]\hrulefill[/tex]
Question 2
The given table is a grouped frequency table, showing the weights of 30 stones to the nearest tenth of an ounce.
Grouped frequency tables show the number of observations whose values fall within certain classes. Notice how grouped frequency tables don’t tell you the exact value of the observations - just the most and the least they could be.
The lightest stone that could go in the 1.7-2.1 class would actually be 1.65 oz, since 1.65 rounds up to 1.7.
Therefore, we cannot label the first class "less than 1.7" since a stone that is 1.65 oz is less than 1.7 but would go into the second 1.7-2.1 class.
Therefore, for the cumulative frequency table, we need to keep the "weight column" the same as in the grouped frequency table.
Cumulative frequency refers to the running total of frequencies in a dataset. It is calculated by adding up the frequencies in ascending order.
[tex]\begin{array}{c|c|r}&\sf Number&\sf Cumulative\\\sf Weight\;(oz)&\sf of\;stones&\sf Frequency\\\cline{1-3} 1.2-1.6&5&5\\1.7-2.1&2&5+2=7\\ 2.2-2.6 & 5 &7+5= 12\\2.7-3.1 & 5 & 12+5=17\\3.2-3.6 & 13 & 17+13=30\end{array}[/tex]
Therefore, the cumulative frequency distribution that corresponds to the given frequency distribution can only be:
[tex]\begin{array}{c|c}&\sf Cumulative\\\sf Weight\;(oz)&\sf Frequency\\\cline{1-2} 1.2-1.6&5\\1.7-2.1&7\\ 2.2-2.6 & 12\\2.7-3.1 & 17\\3.2-3.6 & 30 \end{array}[/tex]
