median is 79.
Write in order; median is middle number:
{72, 89, 67, 81, 75, 79, 81, 80, 62, 64, 83}
→ {62, 64, 67, 72, 75, 79, 80, 81, 81, 83, 89}
To find middle number, count the number of data items, add 1 and divide by 2.
If this is a whole number, that is the data item which is the median; if it is a fraction, take the mean average of the data items of the positions either side of the fraction (eg if the fraction is 3.5, take the mean average of the 3rd and 4th data items)
There are 11 data items → median is (11+1)/2 = 6th data item
→ median is 79
step 1. arrange the numbers in ascending order (from low to high) as follows. was: 64 80 64 70 76 79 67 72 65 73 68 65 67 65 70 62 67 68 65 64 now: 62 64 64 64 65 65 65 65 67 67 67 68 68 70 70 72 73 76 79 80 step 2. count the number of the numbers above, or assign an index as follows. string: 62 64 64 64 65 65 65 65 67 67 67 68 68 70 70 72 73 76 79 80 index: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 so the count is 20. The mode is the number most frequently observed. The mode is 65, which occurs four times. The median is the number in the middle. In this case, the 10th and 11th numbers both qualify for consideration. We take the average of the two numbers. The median is therefore 67. Alternate methods: 1) Use Microsoft Excel statistical functions of =mode() and =median() 2) Draw a bar graph with the horizontal axis of integers from 62 to 80. The y-axis is the frequency observed for that specific x value. For example, the frequency for 62 is one. The frequency for 63 is zero, and so on. The mode is the bar with the highest count. The median is not so obvious from a bar graph, unless the distribution is symmetric. Need some manual counting.
It is 68, the number in the middle when they are arranged in order.
There are 14 numbers - therefore, the median number is halfway between the seventh and eighth number. This is therefore 70.5.
find varience fo rthis numbers 71, 67, 70, 59, 71, 68, 67, 71, 80, 68, 74, 69, 72, 68.
62 64 66 68 70 72
step 1. arrange the numbers in ascending order (from low to high) as follows. was: 64 80 64 70 76 79 67 72 65 73 68 65 67 65 70 62 67 68 65 64 now: 62 64 64 64 65 65 65 65 67 67 67 68 68 70 70 72 73 76 79 80 step 2. count the number of the numbers above, or assign an index as follows. string: 62 64 64 64 65 65 65 65 67 67 67 68 68 70 70 72 73 76 79 80 index: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 so the count is 20. The mode is the number most frequently observed. The mode is 65, which occurs four times. The median is the number in the middle. In this case, the 10th and 11th numbers both qualify for consideration. We take the average of the two numbers. The median is therefore 67. Alternate methods: 1) Use Microsoft Excel statistical functions of =mode() and =median() 2) Draw a bar graph with the horizontal axis of integers from 62 to 80. The y-axis is the frequency observed for that specific x value. For example, the frequency for 62 is one. The frequency for 63 is zero, and so on. The mode is the bar with the highest count. The median is not so obvious from a bar graph, unless the distribution is symmetric. Need some manual counting.
It is 68, the number in the middle when they are arranged in order.
I guess you mean: What is the median of the numbers 71, 67, 67, 72, 76, 73, 68, 72, 72? (because adding the numbers would yield a single number). The median is the middle number when the numbers are listed in order. Listing in order: 71, 67, 67, 72, 76, 73, 68, 72, 72 ⇒ 67, 67, 68, 71, 72, 72, 72, 73, 76 There are 9 numbers, so the middle number is the 5th one which is 72. If there had been an even number of numbers, there is no middle one so the median is the mean average of the middle two. Example: If there had been no 76, so the list contained: 67, 67, 68, 71, 72, 72, 72, 73 then there would be 8 numbers, so the median would be the mean average of the 4th and 5th numbers, namely: (71 + 72) ÷ 2 = 71.5
There are 14 numbers - therefore, the median number is halfway between the seventh and eighth number. This is therefore 70.5.
64 64 64 65 65 65 65 67 67 68 68 70 70 72 73 76 79 80. NB Place the numbers in RANK order. In this case it is already done #1 MODE ; is the term that occurs most frequently. In this case it is '65' , as there are four lots of '65' #2 MEDIAN ; is the term that occurs at the ABSOLUTE middle of the ranked order. Since there are eighteen terms, there is no absolute middle term. So we take the two middle terms that have the same number of terms to their side, that is terms nine & ten. They are 67 & 68. We then add these two together and halve the result. Hence (67 + 68) / 2 = 67.5. This is the median term. #3 MEAN ; is the sum of all the terms, which is the divided by the number of terms. Hence (64+64+64+65+65+65+65+67+67+68+68+70+70+72+73+76+79+80)/18 = 69' NB Another way of calculating the mean is ((3x64)+(4x65)+(2x67)+(2x68)+(2x70)+72+73+76+79+80)/18 = 69 NNB The word 'average' is casually used in the non-mathematical world, but the correct term is MEAN.
It is: 69
80
find varience fo rthis numbers 71, 67, 70, 59, 71, 68, 67, 71, 80, 68, 74, 69, 72, 68.
49, 36, 25 and 64 are all squares of whole numbers. 64 = 82 49 = 72 36 = 62 25 = 52 The square root of 72 is not a whole number, but approximately 8.48. Thus 72 is the "odd one out".
Median is: (54+72)/2 = 63.
62 64 66 68 70 72
72