题目

Problem

The weights, to the nearest kilogram, of a sample of 33 female spotted hyenas living in the Serengeti are summarised in the stem and leaf diagram below.

Key: $3\mid2$ means 32

(a) Find the median and quartiles for the weights of the female spotted hyenas.

(3)

An outlier is defined as any value greater than $c$ or any value less than $d$ where

c=Q_3+1.5(Q_3-Q_1),\qquad d=Q_1-1.5(Q_3-Q_1)

(b) Showing your working clearly, identify any outliers for these data.

(3)

The weights, to the nearest kilogram, of a sample of male spotted hyenas living in the Serengeti are summarised below.

(c) In the space provided in the grid above, draw a box and whisker plot to represent the weights of female spotted hyenas living in the Serengeti. Indicate clearly any outliers.

(3)

(d) Compare the weights of male and female spotted hyenas living in the Serengeti.

(2)

解答

解法一

思路

展开

共有 33 个数据，中位数是第 17 个。上下四分位数分别取下半部分和上半部分的中位数。

答题过程

展开

There are $33$ values, so the median is the 17th value:

\begin{align*} Q_2=54. \end{align*}

The lower quartile is the median of the first 16 values:

\begin{align*} Q_1=\frac{45+45}{2}=45. \end{align*}

The upper quartile is the median of the last 16 values:

\begin{align*} Q_3=\frac{59+59}{2}=59. \end{align*}

Hence

\begin{align*} \operatorname{IQR}=59-45=14. \end{align*}

The outlier limits are

\begin{align*} c=59+1.5(14)=80 \end{align*}

and

\begin{align*} d=45-1.5(14)=24. \end{align*}

So the only outlier is

\begin{align*} 84. \end{align*}

The female box plot should have a box from $45$ to $59$ , median $54$ , whiskers to $32$ and $77$ , and an outlier at $84$ .

Compared with the males, the female hyenas tend to be heavier because their median weight is higher. The male weights have a slightly larger spread, since their whiskers extend over a wider range.

IAL 2018 Oct Q2

题目

解答

解法一

思路

答题过程