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1(a) Mean: 4.71 SD: 2.61 (to 3 sf)

(b) New mean : 5.7

The mean increased by 0.99 (5.7-4.71)

(c) New SD: 2.866

The SD increased by 0.256 (2.866-2.61)

In conclusion, the football players are more fit than the Sec4 boys as the mean of the amount of their pull up was more than then Sec4 boys.

2(a) Mean:5 SD:1.69

(b) New Mean: 5.05 New SD: 1.959

The mean increased by .05 while the SD increased by .890

3. When the spread of data increases, the SD also increases

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1 (a) Mean = 4.71 SD = 2.61

New Mean : 5.7 New SD: 2.87.

(b) Therefore, the mean had increased by 0.99. (c) The standard deviation also increased by 0.259

2)(a) Mean: 5.0 SD:1.69

(b) New Mean: 5.05 New SD: 1.959

Thereby, the mean increases from 5.0 to 5.05 by 0.05. The SD had increased from 1.69 to 1.959 by 0.269.

3) The higher the standard deviation, the more wide spread the data will be.The lower the standard deviation, the closer the data is to the mean.

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1. (a) Mean : 4.71 SD : 2.607

(b) New mean : 5.7 (the mean increased by 0.99)

(c) New SD : 2.866 (The SD increased by 0.259)

2. (a) Mean : 5.0 SD : 1.69

(b) New Mean : 5.05 ( mean increased by 0.5)

New SD : 1.959 ( SD increased by 0.269)

(c) The wider the spread of the data, the larger the amount of standard deviation. The less wider the spread of the data, the lesser the amount of standard deviation.

The 'standard deviation' in statistics or probability is a measure of how spread the mean is.

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1a ) mean=4.71 SD=2.61

b) new mean=5.7 SD=2.87 . Therefore the mean increases.

1c) the standard deviation also increases and therefore becoming more widespread

2a) mean=5.0 SD=1.69

b)mean=5.05 SD=1.96

and so the mean and the standard deviation increases

3)The more the SD increases, the more widespread the data becomes

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Standard deviation is a widely used measurement of variability or diversity. It shows how much variation from the "average" (mean, or expected/budgeted value). A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data is spread out over a large range of values.

1. (a) Mean=4.71 SD=2.607 New Mean: 5.7 New SD= 2.866 (b)The Mean had increased by 0.99 as compared to the previous data. (5.7-4.71 = 0.99) (c) It made the Standard Deviation more widespread. (2.866-2.607 = 0.259) 2. (a) Mean=5.0 SD=1.69 New Mean= 5.05 New SD=1.69 (b) The Mean had increased by 0.05 as compared to the previous data. (5.05-5.0=0.05) (c) It made the Standard Deviation more widespread. (1.959-1.69 =0.269) 3. The wider the spread of data, the higher the Standard Deviation.

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Definition of Mean :
The mean is the average of the numbers: a calculated "central" value of a set of numbers'.

Definition of Standard Deviation :

'A quantity expressing by how much the members of a group differ from the mean value for the group'.

1. (b) Mean=4.71 SD=2.61 √.

(b) New mean=5.7  √.

[The mean increases by 0.99] .

(c) New SD=2.87

[The standard deviation increases by 0.19]

2. (a) Mean=5.0, SD=1.69

(b) New Mean=5.05

[The mean increases by 0.05]

New SD=1.96

[The standard deviation increases by 0.27]

3. The wider the spread of the data, the higher the amount of standard deviation.

↓The diagram below is an example of a Standard Deviation graph. ↓

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Go to www.padlet.com/wall/SDLesson

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This is a wall to host the YouTube url links for education videos on using the various calculators to find mean and standard deviation (SD).

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Applet: Go to    http://www.math.usu.edu/~schneit/CTIS/SD/index.html

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Applet: Go to    http://www.math.usu.edu/~schneit/CTIS/SD/index.html

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Use the applet listed or you can compute the mean and standard deviation by calculator to answer the following questions

1. Pull-Up Data:

The following data was observed by a PE teacher, of the number of pull-ups by Sec 4 boys at

ABC School. Use the Standard Deviation Applet to record this data. Increase the columns to 10. Click show values

Once you have entered the data record the mean and standard deviation:

2, 3, 4, 3, 2, 5, 5, 6, 6, 6, 9, 4, 10, 3, 2, 1, 9.

(a) Mean:_____________________ Standard Deviation:________________________

Six of the school football players were absent on the day that the pull-up test was given, they took the pull-ups test another day and their results are 7, 7, 8, 10, 10, 9.  Add these points to your bar graph.

(b) How did these points change the mean?

(c) How did these new data points change the Standard Deviation?

2. Car Data:

The following data was observed by the LTA officer. The officer recorded the number of cars that went through an intersection for each green light. The following is his data set on a given hour:

4, 5, 3, 6, 7, 8, 5, 6, 7, 2, 3, 6, 4, 4

(a) Mean:_____________________ Standard Deviation:________________________

Deciding that he didn’t have enough data from his first set of observations the officer decided to go back to the intersection and observe a few more data points. The results of this data are:

5, 9, 7, 3, 2. Add these data points to your existing graph.

(b) What are the mean and standard deviation now? How did they change?

3. Analysis:

What is the relationship between the spread of the data and the standard deviation?