Std-deviation

Calculate standard deviation for file:

63,65,68,69,69,72,75,76,77,79,79,80,82,83,84,88,90

Correct answer:

s =  7.6561
s₁ =  7.8917

Step-by-step explanation:

$$\begin{gathered} n=17 \\ m=(63+65+68+69+69+72+75+76+77+79+79+80+82+83+84+88+90)\mathrm{/}n=(63+65+68+69+69+72+75+76+77+79+79+80+82+83+84+88+90)\mathrm{/}17={\displaystyle \frac{1299}{17}}=76\frac{7}{17}\doteq 76.4118 \\ {a}_1=(63-m{)}^2=(63-76.4118{)}^2\doteq 179.8754 \\ {a}_2=a_1+(65-m{)}^2=179.8754+(65-76.4118{)}^2\doteq 310.1038 \\ {a}_3=a_2+(68-m{)}^2=310.1038+(68-76.4118{)}^2\doteq 380.8616 \\ {a}_4=a_3+(69-m{)}^2=380.8616+(69-76.4118{)}^2\doteq 435.7958 \\ {a}_5=a_4+(69-m{)}^2=435.7958+(69-76.4118{)}^2\doteq 490.7301 \\ {a}_6=a_5+(72-m{)}^2=490.7301+(72-76.4118{)}^2\doteq 510.1938 \\ {a}_7=a_6+(75-m{)}^2=510.1938+(75-76.4118{)}^2\doteq 512.1869 \\ {a}_8=a_7+(76-m{)}^2=512.1869+(76-76.4118{)}^2\doteq 512.3564 \\ {a}_9=a_8+(79-m{)}^2=512.3564+(79-76.4118{)}^2\doteq 519.0554 \\ {a}_{10}=a_9+(79-m{)}^2=519.0554+(79-76.4118{)}^2\doteq 525.7543 \\ {a}_{11}=a_{10}+(79-m{)}^2=525.7543+(79-76.4118{)}^2\doteq 532.4533 \\ {a}_{12}=a_{11}+(80-m{)}^2=532.4533+(80-76.4118{)}^2\doteq 545.3287 \\ {a}_{13}=a_{12}+(82-m{)}^2=545.3287+(82-76.4118{)}^2\doteq 576.5571 \\ {a}_{14}=a_{13}+(83-m{)}^2=576.5571+(83-76.4118{)}^2\doteq 619.9619 \\ {a}_{15}=a_{14}+(84-m{)}^2=619.9619+(84-76.4118{)}^2\doteq 677.5433 \\ {a}_{16}=a_{15}+(88-m{)}^2=677.5433+(88-76.4118{)}^2\doteq 811.8304 \\ {a}_{17}=a_{16}+(90-m{)}^2=811.8304+(90-76.4118{)}^2={\displaystyle \frac{16940}{17}}=996\frac{8}{17}\doteq 996.4706 \\ s=\sqrt{a_{17}\mathrm{/}n}=\sqrt{996.4706\mathrm{/}17}=7.6561 \end{gathered}$$

$s_1=\sqrt{a_{17}\mathrm{/}(n-1)}=\sqrt{996.4706\mathrm{/}(17-1)}=7.8917$

Try another example

Showing 1 comment:

Dr Math

See also our standard deviation calculator for this case:

https://www.hackmath.net/en/calculator/standard-deviation?input=63%2C65%2C68%2C69%2C69%2C72%2C75%2C76%2C77%2C79%2C79%2C80%2C82%2C83%2C84%2C88%2C90

Statistical file:
{63, 65, 68, 69, 69, 72, 75, 76, 77, 79, 79, 80, 82, 83, 84, 88, 90}

Standard deviation σ=7.63165870128
Corrected sample standard deviation s=7.86653373101

2 years ago  Like

Related math problems and questions:

• 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
• 75th percentile (quartille Q3)
  Find 75th percentile for 30,42,42,46,46,46,50,50,54
• Alcohol 2
  Two types of alcohol one 63% and second 75% give 20 liters of 69% alcohol. How many liters of each type are in the mixture?
• Annual income
  The annual income (in thousands of $) of fifteen families is 60, 80, 90, 96, 120, 150, 200, 360, 480, 520, 1060, 1200, 1450, 2500, 7200. Calculate the harmonic and geometric mean.
• Reverse Pythagorean theorem
  Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
• Basketball team
  The heights of five starters on redwood high’s basketball team are 5’11”, 6’3”, 6’6”, 6’2” and 6’. The average of height of these players is?
• Alcohol mixing
  How much 64% of the alcohol must be poured into 6 liters of 85% alcohol to produce 79% alcohol?
• 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?
• Final exam
  There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage?
• Tallest people a
  As a group, the Dutch are amongst the tallest people in the world. The average Dutchman is 184 cm tall. If a normal distribution is appropriate, and the standard deviation for Dutchmen is about 8 cm, what is the percentage of Dutchmen who will be over 2 m
• A mountain
  A mountain climber plans to buy some rope to use as lifeline. Which of the following would be the better choice? Explain your choice. Rope A: Mean breaking strength:500lb; standard deviation of 100lb Rope B: Mean breaking strength: 500lb; standard deviati
• Chess
  How many ways can select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
• Mastering
  The student masters the subject matter for the exam in Czech to 98%, from Math to 86% and from Economics to 71%. What is the probability that he will fail from Math and from others will succeed?
• Statistical XY file
  Year; money spent on advertising; profit (three values each row) 2008 2 12 2009 5 20 2010 7 25 2011 11 26 2012 15 40 1. draw a scatter diagram depicting the data. 2. calculate the Pearson's correlation coefficient. 3. determine the linear regression equat
• Box and whisker plot
  Construct a box and whisker plot for the given data. 56, 32, 54, 32, 23, 67, 23, 45, 12, 32, 34, 24, 36, 47, 19, 43
• Triangles
  Find out whether given sizes of the angles can be interior angles of a triangle: a) 23°10',84°30',72°20' b) 90°,41°33',48°37' c) 14°51',90°,75°49' d) 58°58',59°59',60°3'
• Exponential decay
  A tank contains 55 liters of water. Water is flowing out at the rate of 7% per minute. How long does it take to drain the tank?