Notes for Chapter 1
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Chapter 1 Statistics
Real World Use of Whole Numbers
Bar Graph – uses vertical or horizontal bars to represent data and display numerical information. The height or length of the bar tells you the number/amount it represents. The bars never touch. Bar graphs always start with zero. All graphs must have labels.
Pictograph – uses symbols/pictures to represent data. All symbols have the same value. A key tells/shows how much each symbol represents. To determine the measure of an item, count the number of symbols and multiply by the value.
Line Graph – often shows how data changes over time. Each dot represents a specific value of an item of data. The height of the dot represents the value of the data. The time is shown by how far to the right the dot is.
Circle Graph – show how portions of a set of data compare with the whole/total set (100%). The larger the value of the data, the larger the wedge that represents the data.
Interval – the amount of space between values on the X and Y axis.
Scatterplot – a graph that shows paired data. Each point represents two data values.
Trend – a relationship between two sets of data that shows a pattern.
Upward Trend – both values get larger together.
Downward Trend – “x” values get bigger while “y” values get smaller.
No Trend – random; no pattern.
Tally – each tally mark indicates one time the value appears in the data.
Frequency Chart – lists each value by the number of times it appears.
Line Plot – shows the shape of a data set. It uses Xs instead of tally marks.
Tally Chart Frequency Chart Line Plot
↓ ↓ ↓
Age|Tally Age|Frequency
5 | 1111 5 | 4 x
6 | 11111 111 6 | 8 x
7 | 11111 11111 7 | 10 x x
8 | 11 8 | 2 x x
x x
x x
x x x
x x x
x x x x
x x x x
_______________________________
0 1 2 3 4 5 6 7 8 9
Stem and Leaf Diagram – a graph that shows the shape of the data according to the data place value. The “leaf” of a number is the right hand digit (ones place value). The “stem” is the portion of the number to the left of the leaf Hint: It may be helpful to plot all the stems before the leaf.
Data Set: 2, 3, 7, 11, 12, 19, 30 Stem | Leaf
0 | 2, 3, 7
1 | 1, 2, 9
3 | 0
*All stem and leaf diagrams must have a key.
*Key S | L
3 | 0 = 30
Range – arrange numbers from lowest to highest, (i.e., the range of grades is 81 to 100. The range of a data set also refers to the difference between the highest value and the lowest value, (i.e., the highest is 100 and the lowest is 81; subtract 100 – 81 = 19, therefore, the range is also 19).
Median – of a data set isthe middle number when the data is listed from lowest to highest, (i.e., in the data set: 1, 5, 6, 8, 9, 11, 15 the middle number is 8, therefore, the median is 8).
If the set has two middle numbers, add the numbers and divide by 2, (i.e., in the data set: 1, 5, 6, 8, 9, 11, there are two middle numbers, 6 and 8;
add 6 + 8 = 14 and divide 14 ÷ 2 = 7, therefore, the median is 7).
Sometimes you may end up with an odd number when you add two middle numbers, (i.e., in the data set: 1, 5, 6, 15, 16, 17, when you add the two middle numbers 6 and 15, the answer, 21, is an odd number, therefore when you divide by 2 (21 ÷ 2 = 10.5), the median will be a decimal (10.5) or it can be stated as a fraction 10 .
Mode – the number that appears most often in a set of data, (i.e., in the data set: 1, 2, 3, 3, 3, 5, 5, the mode is 3).
Some data sets have no modes, (i.e., in the data set: 1, 2, 3, 4, 5, there is no mode).
Some data sets have more than one mode, (i.e., in the data set: 1, 2, 2, 3, 3, 4, 4, 6, the mode = 2, 3, and 4).
Mean – of a data set is a sum of the items in a set divided by number of items, (i.e., in the data set: 2, 3, 6, 6, 8, add all the numbers,
2 + 3 + 6 + 6 + 8 = 25 and divide by how many numbers are in the set,
25 ÷ 5 = 5, therefore, the mean is 5). The mean can also be referred to as the average.
Outlier – a number in a data set that is very different from the rest of the numbers. Outliers can have a big effect on the mean.
i.e.: in the data set: 87, 95, 80, 97, 80, 83, the average is 87 (522 ÷ 6 = 87), however, if one of the test scores changes from 80 to 40, the average of the data set: 87, 95, 40, 97, 80, 83 will be 80 (482 ÷÷ 6 = 80).
Real World Use of Whole Numbers
Bar Graph – uses vertical or horizontal bars to represent data and display numerical information. The height or length of the bar tells you the number/amount it represents. The bars never touch. Bar graphs always start with zero. All graphs must have labels.
Pictograph – uses symbols/pictures to represent data. All symbols have the same value. A key tells/shows how much each symbol represents. To determine the measure of an item, count the number of symbols and multiply by the value.
Line Graph – often shows how data changes over time. Each dot represents a specific value of an item of data. The height of the dot represents the value of the data. The time is shown by how far to the right the dot is.
Circle Graph – show how portions of a set of data compare with the whole/total set (100%). The larger the value of the data, the larger the wedge that represents the data.
Interval – the amount of space between values on the X and Y axis.
Scatterplot – a graph that shows paired data. Each point represents two data values.
Trend – a relationship between two sets of data that shows a pattern.
Upward Trend – both values get larger together.
Downward Trend – “x” values get bigger while “y” values get smaller.
No Trend – random; no pattern.
Tally – each tally mark indicates one time the value appears in the data.
Frequency Chart – lists each value by the number of times it appears.
Line Plot – shows the shape of a data set. It uses Xs instead of tally marks.
Tally Chart Frequency Chart Line Plot
↓ ↓ ↓
Age|Tally Age|Frequency
5 | 1111 5 | 4 x
6 | 11111 111 6 | 8 x
7 | 11111 11111 7 | 10 x x
8 | 11 8 | 2 x x
x x
x x
x x x
x x x
x x x x
x x x x
_______________________________
0 1 2 3 4 5 6 7 8 9
Stem and Leaf Diagram – a graph that shows the shape of the data according to the data place value. The “leaf” of a number is the right hand digit (ones place value). The “stem” is the portion of the number to the left of the leaf Hint: It may be helpful to plot all the stems before the leaf.
Data Set: 2, 3, 7, 11, 12, 19, 30 Stem | Leaf
0 | 2, 3, 7
1 | 1, 2, 9
3 | 0
*All stem and leaf diagrams must have a key.
*Key S | L
3 | 0 = 30
Range – arrange numbers from lowest to highest, (i.e., the range of grades is 81 to 100. The range of a data set also refers to the difference between the highest value and the lowest value, (i.e., the highest is 100 and the lowest is 81; subtract 100 – 81 = 19, therefore, the range is also 19).
Median – of a data set isthe middle number when the data is listed from lowest to highest, (i.e., in the data set: 1, 5, 6, 8, 9, 11, 15 the middle number is 8, therefore, the median is 8).
If the set has two middle numbers, add the numbers and divide by 2, (i.e., in the data set: 1, 5, 6, 8, 9, 11, there are two middle numbers, 6 and 8;
add 6 + 8 = 14 and divide 14 ÷ 2 = 7, therefore, the median is 7).
Sometimes you may end up with an odd number when you add two middle numbers, (i.e., in the data set: 1, 5, 6, 15, 16, 17, when you add the two middle numbers 6 and 15, the answer, 21, is an odd number, therefore when you divide by 2 (21 ÷ 2 = 10.5), the median will be a decimal (10.5) or it can be stated as a fraction 10 .
Mode – the number that appears most often in a set of data, (i.e., in the data set: 1, 2, 3, 3, 3, 5, 5, the mode is 3).
Some data sets have no modes, (i.e., in the data set: 1, 2, 3, 4, 5, there is no mode).
Some data sets have more than one mode, (i.e., in the data set: 1, 2, 2, 3, 3, 4, 4, 6, the mode = 2, 3, and 4).
Mean – of a data set is a sum of the items in a set divided by number of items, (i.e., in the data set: 2, 3, 6, 6, 8, add all the numbers,
2 + 3 + 6 + 6 + 8 = 25 and divide by how many numbers are in the set,
25 ÷ 5 = 5, therefore, the mean is 5). The mean can also be referred to as the average.
Outlier – a number in a data set that is very different from the rest of the numbers. Outliers can have a big effect on the mean.
i.e.: in the data set: 87, 95, 80, 97, 80, 83, the average is 87 (522 ÷ 6 = 87), however, if one of the test scores changes from 80 to 40, the average of the data set: 87, 95, 40, 97, 80, 83 will be 80 (482 ÷÷ 6 = 80).