Variability

In the table bellow the number of wrong produced goods in two shifts: morning shift: 2; 0; 6; 10; 2; 2; 4; 2; 5; 2; afternoon shift: 4; 4; 0; 2; 10; 2; 6; 2; 3; 10; Compare the variability in both shifts, compare the average number of wrong goods on both shifts as well as other variability and positioning rates.

Correct answer:

a₁ =  3.5
a₂ =  4.3
s₁ =  2.7295
s₂ =  3.2265

Step-by-step explanation:

$a_1=(2+0+6+10+2+2+4+2+5+2)\mathrm{/}10=3.5$

$$\begin{gathered} a_2=(4+4+0+2+10+2+6+2+3+10)\mathrm{/}10={\displaystyle \frac{43}{10}}=4\frac{3}{10}=4.3 \\ {a}_2>a_1 \end{gathered}$$

$$\begin{gathered} b_1=(2-a_1{)}^2+(0-a_1{)}^2+(6-a_1{)}^2+(10-a_1{)}^2+(2-a_1{)}^2+(2-a_1{)}^2+(4-a_1{)}^2+(2-a_1{)}^2+(5-a_1{)}^2+(2-a_1{)}^2=(2-3.5{)}^2+(0-3.5{)}^2+(6-3.5{)}^2+(10-3.5{)}^2+(2-3.5{)}^2+(2-3.5{)}^2+(4-3.5{)}^2+(2-3.5{)}^2+(5-3.5{)}^2+(2-3.5{)}^2={\displaystyle \frac{149}{2}}=74\frac{1}{2}=74.5 \\ {r}_1=1\mathrm{/}10\cdot b_1=1\mathrm{/}10\cdot 74.5={\displaystyle \frac{149}{20}}=7\frac{9}{20}=7.45 \\ {s}_1=\sqrt{r_1}=\sqrt{7.45}=2.7295 \end{gathered}$$

$$\begin{gathered} b_2=(4-a_2{)}^2+(4-a_2{)}^2+(0-a_2{)}^2+(2-a_2{)}^2+(10-a_2{)}^2+(2-a_2{)}^2+(6-a_2{)}^2+(2-a_2{)}^2+(3-a_2{)}^2+(10-a_2{)}^2=(4-4.3{)}^2+(4-4.3{)}^2+(0-4.3{)}^2+(2-4.3{)}^2+(10-4.3{)}^2+(2-4.3{)}^2+(6-4.3{)}^2+(2-4.3{)}^2+(3-4.3{)}^2+(10-4.3{)}^2={\displaystyle \frac{1041}{10}}=104\frac{1}{10}=104.1 \\ {r}_2=1\mathrm{/}10\cdot b_2=1\mathrm{/}10\cdot 104.1={\displaystyle \frac{1041}{100}}=10\frac{41}{100}=10.41 \\ {s}_2=\sqrt{r_2}=\sqrt{10.41}\doteq 3.2265 \\ {s}_2>s_1 \end{gathered}$$

Try another example

Related math problems and questions:

• Complaints
  The table is given: days complaints 0-4 2 5-9 4 10-14 8 15-19 6 20-24 4 25-29 3 30-34 3 1.1 What percentage of complaints were resolved within 2weeks? 1.2 calculate the mean number of days to resolve these complaints. 1.3 calculate the modal number of day
• Standard deviation
  Find standard deviation for dataset (grouped data): Age (years) No. Of Persons 0-10 15 10-20 15 20-30 23 30-40 22 40-50 25 50-60 10 60-70 5 70-80 10
• Chi square
  A manufacturer of phone batteries claims that his batteries' lives are approximately normally distributed with a standard deviation equal to 0.9 years. If a random sample of 10 of these batteries has a standard deviation of 1.2 years. Do you think that th
• Unemployment rate
  Over the last 16 years, the country's unemployment rate has changed according to the following frequency table: years of unemployment: 2 5 2 3 3 1 unemployment rate: 0.5 1 1.5 2 2.5 3 in % (percent). Determine the two-sided confidence interval for the var
• Median or middle
  The number of hours of television watched per day by a sample of 28 people is given below: 4, 1, 5, 5, 2, 5, 4, 4, 2, 3, 6, 8, 3, 5, 2, 0, 3, 5, 9, 4, 5, 2, 1, 3, 4, 7, 2, 9 What is the median value?
• Confidence Interval
  The average grade of 50 students senior students in a statistics class is 85 with a standard deviation of 10.2 while a group of 60 senior students got an average of 80 with a standard deviation of 8.9, can the difference in the mean grade be attributed to
• The accompanying
  The accompanying table gives the probability distribution of the number of courses randomly selected student has registered Number of courses 1 2 3 4 5 6 7 Probability 0.02 0.03 0.1 0.3 0.4 - 0.01 respectively. a) Find the probability of a student registe
• Contestants
  In the competition it was possible to get 0-5 points. In fact, 5 contestants of the 15 best contestants has earned 5 points or 4 points (which have won 10 contestants). The number of contestants who earned 3 points was the same as the number of contestant
• Decimal expansion
  Calculate: 2 . 1 + 0 . 10 + 7 . 10000 + 4 . 1000 + 6 . 100 + 0 . 100000 =
• Pure quadratic equation
  Solve pure quadratic equation -5x² +10 = 0.
• Normal Distribution
  At one college, GPA's are normally distributed with a mean of 3.1 and a standard deviation of 0.4. What percentage of students at the college have a GPA between 2.7 and 3.5?
• Center
  Calculate the coordinates of the circle center: x² -4x + y² +10y +25 = 0
• SD - mean
  The mean is 10 and the standard deviation is 3.5. If the data set contains 40 data values, approximately how many of the data values will fall within the range of 6.5 to 13.5?
• Five number summary
  Find the five-number summary for these data and make a boxplot. 14,5,12,19,2,35,5,4,3,7,5,8
• Pool
  If water flows into the pool by two inlets, fill the whole for 19 hours. The first inlet filled pool 5 hour longer than the second. How long pool take to fill with two inlets separately?
• In the
  In the 6th class, the average half-year mark in physics was 1.7. At the end of the year, Maťo improved his mark from 2 to 1, Ivanka from 3 to 2, and Elenka from 4 to 2. Pavlík worsened his mark from 3 to 4. The average mark of the whole class thus improve
• The temperature
  The temperature at 1:00 was 10 F. Between 1:00 and 2:00, the temperature dropped 15F. Between 2:00 and 3:00, the temperature rose 3F. What is the temperature at 3:00?