Here's the general rule for rounding: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. Example: 38 rounded to the nearest ten is 40. If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down.
There are two steps to finding the mean, or averaging numbers; they are, first, to add up the series of numbers you have and, second, to divide the sum by the number of numbers in the series. Let's go through an example so that you can see each step. Here is our series: 7, 9, 2, 4, 13, 9, 17.
Whenever the decimal value you intend to round off is 5, you must look at the previous values, before decimals ALSO. If it is an even number, then you round it down and if it is an odd number, you round it up. For example, in the case given above, in 2345.5, the number preceding .
And you round to the nearest percent. Now the rounding begins. We look at the number to the right of the 4, namely the second 1. If it's 4 or less, you round down.
Mode (statistics) The mode of a set of data values is the value that appears most often. If X is a discrete random variable, the mode is the value x (i.e, X = x) at which the probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.
If the standard deviation were 20", then some men would be much taller or much shorter than the average, with a typical range of about 50"–90". For another example, each of the three groups {0, 0, 14, 14}, {0, 6, 8, 14} and {6, 6, 8, 8} has an average (mean) of 7.
A suitable rule specifies up to one decimal place and up to two significant digits. When comparing group means or percentages in tables, rounding should not blur the differences between them.
To round off decimals:
- Find the place value you want (the "rounding digit") and look at the digit just to the right of it.
- If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.
Note: It is possible for a set of data values to have more than one mode. If there are two data values that occur most frequently, we say that the set of data values is bimodal. If there is no data value or data values that occur most frequently, we say that the set of data values has no mode.
To find the median, your numbers have to be listed in numerical order from smallest to largest, so you may have to rewrite your list before you can find the median. The "mode" is the value that occurs most often. If no number in the list is repeated, then there is no mode for the list.
In a set of data, the mode is the most frequently observed data value. There may be no mode if no value appears more than any other. There may also be two modes (bimodal), three modes (trimodal), or four or more modes (multimodal).
If there are two numbers that appear most often (and the same number of times) then the data has two modes. This is called bimodal. If there are more than 2 then the data would be called multimodal. If all the numbers appear the same number of times, then the data set has no modes.
In this case you divide the total count of numbers by 2, and then round UP to the nearest number. This is your median number, because it is in the middle of the set. For instance, if you had a group of 15 numbers in a set, to find the median you would divide 15 by 2.
If there is an even number of numbers locate the two middle numbers so that there is an equal number of values to the left and to the right of these two numbers. Step 3: If there is an odd number of numbers, this middle number is the median. If there is an even number of numbers add the two middles and divide by 2.
You should avoid rounding an expected value to a whole number for a discrete random variable -- E(X) does NOT appear as an outcome for the random variable, but is the weighted mean of all the outcomes by taking into account the probability of each outcome.
Definition: The arithmetic mean of a set of data is found by taking the sum of the data, and then dividing the sum by the total number of values in the set. A mean is commonly referred to as an average. In the problem above, the mean was a whole number. This is not always the case.
Under these circumstances, we can use the following rule for rounding: If the decimal portion is less than 0.5, we round down, if the decimal portion is more than 0.5, we round up, and if the decimal portion is exactly 0.5, we look at the place value to the left of the five (yes, really, the left!).
Intermediate Steps: When performing intermediate steps to do something like calculate the standard deviation, it is best to round to at least one extra decimal place than will be used in the final answer.
The reason is that 5 is directly in the middle of the digits we round, so we must round it up half the time, and down half the time. To make this more clear, look at the digits we round to another number: 1, 2, 3, 4 we round down. Notice that 5, if rounded up always, gives us 5 numbers we round up, and 4 we round down.
The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode!
Rounding Rules for Confidence Intervals
- When you are given a list of raw data you should round the mean and standard deviation to 1 more decimal place than what the data has.
- When calculating confidence intervals for the mean (using z or t), round your margin of error ( E ) to match the number of decimal places in the standard deviation.
Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value. A low standard deviation means that most of the numbers are close to the average. A high standard deviation means that the numbers are more spread out.
As an example, if the precision of a measurement is ±α (say ±0.05, one digit after the decimal point), while we should report mean and SD with the same precision, we need to report the variance (SD2) with two digits after the decimal point (α2 = 0.0025, assuming a large sample size).
The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. The "median" is the "middle" value in the list of numbers.
The Z Score Formula: One Sample
For example, let's say you have a test score of 190. The test has a mean (μ) of 150 and a standard deviation (σ) of 25. Assuming a normal distribution, your z score would be: z = (x – μ) / σWhat is 34519 rounded to the nearest thousands? 34519 rounded off to the nearest thousandth is 35000. In 34519, the hundredth digit is 5 and so, rounding off 34519 to the nearest 1000 result in 35000.
To round to the nearest thousand, we look at the last three digits. If these digits are 500 or greater, then we round the thousands digit up, and if they are less than 500, then we round down, keeping the thousand's digit the same. To round to the nearest ten thousand, we look at the last four digits.
Round 37 to the nearest ten. The digit you're rounding to is the tens digit, 3. 37 is between 30 and 40. 37 is only 3 away from 40, but it's 7 away from 30.
Which number rounded to the nearest 10 is 250
- Answer. 3.3/5.
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So, 75 rounded to the nearest ten is 80 .
13 Rounded to the Nearest Tenth
To round 13 to the nearest tenth consider the hundredths' value of 13, which is 0 and less than 5. Therefore, the tenths value of 13 remains 0.The reason is that 5 is directly in the middle of the digits we round, so we must round it up half the time, and down half the time. To make this more clear, look at the digits we round to another number: 1, 2, 3, 4 we round down. Notice that 5, if rounded up always, gives us 5 numbers we round up, and 4 we round down.
The number "85" is exactly half-way between 80 and 90. If we round this number to the nearest ten, we will round it to 460 (because 462 is closer to 460 than it is to 470).
Answer and Explanation:
The number 63 rounded to the nearest ten is 60.
