prob & stats ch 5b day 4 - boxplots and outliers\nname: natalie mwaga\n1. the following data set shows the…

prob & stats ch 5b day 4 - boxplots and outliers\nname: natalie mwaga\n1. the following data set shows the number of cousins each student in a group has. 0,1,2,4,5,5,7,10,12,13,17,39\n a) determine the five - number summary and iqr: (0,4.5,8.5,12,39)\n b) calculate whether there are any outliers. show work below.\n4.5 - 1.5(7.5)= - 7.75\n12 + 1.5(7.5)=24.25\nlist outliers here, if any: 39\n c) make a well labeled box plot:\n d) find each of the following:\nmean: 9.19\nmode: 5\nrange: 39\nstandard deviation: 9.44\n2. consider the data set below:\n0,8,16,18,19,19,20,20,21,22,25,27,29,33,37,50,54\n a) determine the five - number summary and iqr: (0,19,21,29,54) iqr: 10\n b) calculate whether there are any outliers. show work below.\n19 - 1.5(10)=4\n29 + 1.5(10)=44\nlist outliers here, if any: 0,50,54\n c) make a well labeled box - plot below:\n d) find each of the following:\nmean: 24.59\nmode: 19 and 20\nrange: 54\nstandard deviation: 13.02

prob & stats ch 5b day 4 - boxplots and outliers\nname: natalie mwaga\n1. the following data set shows the number of cousins each student in a group has. 0,1,2,4,5,5,7,10,12,13,17,39\n a) determine the five - number summary and iqr: (0,4.5,8.5,12,39)\n b) calculate whether there are any outliers. show work below.\n4.5 - 1.5(7.5)= - 7.75\n12 + 1.5(7.5)=24.25\nlist outliers here, if any: 39\n c) make a well labeled box plot:\n d) find each of the following:\nmean: 9.19\nmode: 5\nrange: 39\nstandard deviation: 9.44\n2. consider the data set below:\n0,8,16,18,19,19,20,20,21,22,25,27,29,33,37,50,54\n a) determine the five - number summary and iqr: (0,19,21,29,54) iqr: 10\n b) calculate whether there are any outliers. show work below.\n19 - 1.5(10)=4\n29 + 1.5(10)=44\nlist outliers here, if any: 0,50,54\n c) make a well labeled box - plot below:\n d) find each of the following:\nmean: 24.59\nmode: 19 and 20\nrange: 54\nstandard deviation: 13.02

Answer

Explanation:

Step1: Sort the data set

Sort the given data - sets in ascending order for further calculations.

Step2: Calculate the five - number summary

  • Minimum: The smallest value in the data set.
  • First Quartile (Q1): For a data set of size $n$, if $n$ is odd, the position of Q1 is $\frac{n + 1}{4}$, and if $n$ is even, the position is $\frac{n}{4}$. Then, find the corresponding value or the average of two adjacent values.
  • Median (Q2): If $n$ is odd, the median is the middle - value. If $n$ is even, the median is the average of the two middle - values.
  • Third Quartile (Q3): Similar to Q1, but the position is $\frac{3(n + 1)}{4}$ for odd $n$ and $\frac{3n}{4}$ for even $n$.
  • Maximum: The largest value in the data set.

Step3: Calculate the Inter - Quartile Range (IQR)

$IQR=Q3 - Q1$

Step4: Identify outliers

Outliers are values less than $Q1-1.5\times IQR$ or greater than $Q3 + 1.5\times IQR$

Step5: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data points and $n$ is the number of data points.

Step6: Calculate the mode

The mode is the most frequently occurring value in the data set.

Step7: Calculate the range

The range is the difference between the maximum and minimum values in the data set, $Range = Max - Min$

Step8: Calculate the standard deviation

The standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$

Answer:

a) Five - number summary: Minimum = 0, Q1 = 4.5, Median = 8.5, Q3 = 12, Maximum = 39; IQR = 7.5 b) Outliers: 39 c) (Box - plot cannot be shown in text format, but it should have a box from Q1 to Q3 with a line at the median, whiskers from the box to the minimum and maximum non - outlier values, and the outlier 39 marked separately) d) Mean = 9.19, Mode = 5, Range = 39, Standard Deviation = 9.44

a) Five - number summary: Minimum = 0, Q1 = 19, Median = 21, Q3 = 29, Maximum = 54; IQR = 10 b) Outliers: 0, 50, 54 c) (Box - plot cannot be shown in text format, but it should have a box from Q1 to Q3 with a line at the median, whiskers from the box to the minimum and maximum non - outlier values, and the outliers 0, 50, 54 marked separately) d) Mean = 24.59, Mode = 19 and 20, Range = 54, Standard Deviation = 13.02