We can obtain such information by using cumulative frequency. Cumulative frequency is used to determine the number of elements that falls above or below a particular value in a given class interval. The cumulative frequency of a class is calculated by adding its frequency to the sum of all predecessor class frequencies. Consequently, the last value must be equal to the sample size.

The stacked bar chart is a bar chart where each bar is divided into subgroups proportional to the contribution a subgroup makes to associated bar. Likert type items are often represented by stacked bar chart.

Suppose there are n observations; x₁, x₂, x₃, x₄.......x_n, and the arithmetic mean is k. Thus the sum of observations is n*k=(x₁+x₂+x₃+x₄.......+x_n). If we increase all observations by 4, the new values will be 4+x₁, 4+x₂, 4+x₃, 4+x₄.......4+x_n. Thus the new sum will be (4+4+...+4)+(x₁+x₂+x₃+x₄.......+x_n)=4n+nk=n(4+k). If we divide this sum by n then the new arithmetic mean will be 4+k.

In an observational study, researchers simply collect data based on what is seen and heard and infer based on the data collected. Researchers observe subjects and measure variables of interest without any intervention to the subjects. Experimental study is a study in which the researcher manipulates some of the variables and try to determine how the manipulation influences other variables.

In order to find the mode of this raw data, first, let’s order the data from smallest to largest as follows 3,3,4,5,6,6,6,7

The number 3 is repeated 2 times, 4 is repeated 1 time, 5 is repeated 1 time, 6 is repeated 3 time, 7 is repeated 1 time. Therefore, for this data set, it can be said that the mode is 6. The answer is B.

blue is data, not variable.

According to the table, Amanda gets the largest and Liam gets the smallest portion. Therefore, the correct answer is D. 

According to the plot, the maximum value of the data is 97 and the minimum value is 48. Range is the difference between the minimum and the maximum. Thus the rang is 97-48=49. 

Sample in statistics means a small part of the targeted population. A sample must be representative of the population. Sampling methods must be used to achieve a representative sampling. Otherwise, the sampling does not represent the targeted population and the results yield biased or inaccurate information.

Error in population specification occurs when the researcher determines an inappropriate population from which to collect data.

Error in measurement can be described as any discrepancy between the actual result obtained and the correct result that would be provided by an ideal procedure. From a statistical point of view any observation is composed of the true value plus some random error value. However, all error is not random. The error component of any observation can be divided into two subcomponents, random error and systematic error.
Random errors are caused by unknown and unpredictable factors that randomly affect measurement of the variable across the sample. For example, a school teacher conducted a particular survey on the students to measure their performances. Some students may be feeling in a good mood and others may be depressed. This may artificially deflate performance scores of the depressed students. Random error does not have any consistent effects across the entire sample. Instead, it affects observed scores up or down randomly. Random error adds variability to the data and it is sometimes called noise.
Systematic errors are reproducible inaccuracies that shift measurements from their true value by the same amount and consistently in the same direction. This type error arises from problematic, poor calibrated or incorrectly used equipment. For example, an industrial scale showed heavier weights than it should be for a particular product because it was not calibrated properly and thereby provided incorrect measurements.

In stem-and-leaf display the original numbers are kept and a visual representation of data is created. Basically, stem-and-leaf display divides the values into a stem and leaf using a vertical line. The “stem” represents the greatest digits on the left of the line where the right of this line displays the “leaf ” with the remaining digits. This graph can be useful to figure out the range, outliers, the most frequent values and the shape of the data. It is also useful for assessing the location and spread of the distribution of the data.

Likert type of scale is generally used to measure the attitudes of an individual towards a specific subject.

39 : occurs most often, it is repeated 4 times. pg. 81. Correct answer is C.

(20 x 10 % + 40 x 20 % + 60 x 30 % x + 80 x 40 %) / 4 = (2 + 8 + 18 + 32) / 4 = 60 / 4 = 15

This pattern indicates that the days with high humidity tend to have temperatures at 2oC, 5oC, and 8oC.

According to this graph, 2nd and 4th months are the months that equal number of vehicles are registered both in 2017 and 2018. During 2nd month nearly 60 thousand vehicles and during 4th month nearly 100 thousand vehicles were registered. 

qualitative ordinal

Statisticians are the most sought-after professionals these days.We are living in the information age, and the Statistician is the king of handling, analysing, interpreting and facilitating decisions from data. The principal reason why Statistics is a key necessity to humankind today is the massive amounts of available information.