statistics & correlations\npart a: measures of central tendency and range\ndirections: solve the following…

statistics & correlations\npart a: measures of central tendency and range\ndirections: solve the following word problems. show your work.\n1. a psychology professor recorded the number of hours 8 students studied for an exam: 2, 4, 4, 6, 7, 8, 8, 9\n o mean = \n o median = \n o mode = \n o range = \n2. a researcher measured the stress levels (scale 1 - 10) of 6 participants during finals week: 5, 7, 7, 9, 6, 8\n o mean = \n o median = \n o mode = \n o range = \n3. the number of therapy sessions attended by 10 clients over the semester was: 3, 5, 5, 6, 7, 8, 8, 9, 10, 10\n o mean = \n o median = \n o mode = \n o range = \n4. a survey asked how many hours of sleep students got per night during midterms: 4, 5, 5, 6, 6, 6, 7, 8, 9\n o mean = \n o median = \n o mode = \n o range =

statistics & correlations\npart a: measures of central tendency and range\ndirections: solve the following word problems. show your work.\n1. a psychology professor recorded the number of hours 8 students studied for an exam: 2, 4, 4, 6, 7, 8, 8, 9\n o mean = \n o median = \n o mode = \n o range = \n2. a researcher measured the stress levels (scale 1 - 10) of 6 participants during finals week: 5, 7, 7, 9, 6, 8\n o mean = \n o median = \n o mode = \n o range = \n3. the number of therapy sessions attended by 10 clients over the semester was: 3, 5, 5, 6, 7, 8, 8, 9, 10, 10\n o mean = \n o median = \n o mode = \n o range = \n4. a survey asked how many hours of sleep students got per night during midterms: 4, 5, 5, 6, 6, 6, 7, 8, 9\n o mean = \n o median = \n o mode = \n o range =

Answer

Explanation:

Step1: 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.

Problem 1

$n = 8$, $\sum_{i=1}^{8}x_{i}=2 + 4+4 + 6+7 + 8+8 + 9=48$, $\bar{x}=\frac{48}{8}=6$

Problem 2

$n = 6$, $\sum_{i = 1}^{6}x_{i}=5 + 7+7 + 9+6 + 8=42$, $\bar{x}=\frac{42}{6}=7$

Problem 3

$n = 10$, $\sum_{i=1}^{10}x_{i}=3 + 5+5 + 6+7 + 8+8 + 9+10 + 10=71$, $\bar{x}=\frac{71}{10}=7.1$

Problem 4

$n = 9$, $\sum_{i=1}^{9}x_{i}=4 + 5+5 + 6+6 + 6+7 + 8+9=56$, $\bar{x}=\frac{56}{9}\approx6.22$

Step2: Calculate the median

If $n$ is odd, the median is the $\left(\frac{n + 1}{2}\right)$-th ordered data - point. If $n$ is even, the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th ordered data - points.

Problem 1

The data in ascending order: $2,4,4,6,7,8,8,9$. $n = 8$, the median is $\frac{6 + 7}{2}=6.5$

Problem 2

The data in ascending order: $5,6,7,7,8,9$. $n = 6$, the median is $\frac{7+7}{2}=7$

Problem 3

The data in ascending order: $3,5,5,6,7,8,8,9,10,10$. $n = 10$, the median is $\frac{7 + 8}{2}=7.5$

Problem 4

The data in ascending order: $4,5,5,6,6,6,7,8,9$. $n = 9$, the median is the 5 - th value, which is $6$

Step3: Calculate the mode

The mode is the data - point that appears most frequently.

Problem 1

The mode is $4$ and $8$ (bimodal)

Problem 2

The mode is $7$

Problem 3

The mode is $5$, $8$ and $10$ (trimodal)

Problem 4

The mode is $6$

Step4: Calculate the range

The range is the difference between the maximum and minimum values in the data - set, $R=\text{max}-\text{min}$

Problem 1

$\text{max}=9$, $\text{min}=2$, $R=9 - 2=7$

Problem 2

$\text{max}=9$, $\text{min}=5$, $R=9 - 5=4$

Problem 3

$\text{max}=10$, $\text{min}=3$, $R=10 - 3=7$

Problem 4

$\text{max}=9$, $\text{min}=4$, $R=9 - 4=5$

Answer:

  1. Mean = 6, Median = 6.5, Mode = 4, 8, Range = 7
  2. Mean = 7, Median = 7, Mode = 7, Range = 4
  3. Mean = 7.1, Median = 7.5, Mode = 5, 8, 10, Range = 7
  4. Mean $\approx$ 6.22, Median = 6, Mode = 6, Range = 5